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Year 2022, , 199 - 207, 22.12.2022
https://doi.org/10.36753/mathenot.1022886

Abstract

References

  • [1] Lorentz, G.G.: A contribution to the theory of divergent sequences. Acta Math. 80, 167-190 (1948).
  • [2] Bas ̧ar,F.,Kiris ̧çi,M.:Almostconvergenceandgeneralizeddifferencematrix.Comput.Math.Appl.61,602-611(2011).
  • [3] Kiris ̧çi, M.: Almost convergence and generalized weighted mean II. J. Inequal. Appl. 2014 93, (2014).
  • [4] Kiris ̧çi, M.: The spaces of Euler almost null and Euler almost convergent sequences. Commun. Fac. Sci. Univ. Ank. Series A1. 62(2), 85-100 (2013).
  • [5] Mursaleen, M.: Invariant means and some matrix transformations. Indian J. Pure Appl. Math. 25(3), 353-359 (1994).
  • [6] Bas ̧ar, F., Çolak, R.: Almost-conservative matrix transformations. Turkish J. Math. 13(3), 91-100 (1989).
  • [7] Bas ̧ar, F.: f−conservative matrix sequences. Tamkang J. Math. 22(2), 205-212 (1991).
  • [8] Qamaruddin, Q., Mohuiddine, S.A.: Almost convergence and some matrix transformations. Filomat. 21(2), 261-266 (2007).
  • [9] Demiriz,S.,Kara,E.E.,Bas ̧arir,M.:OntheFibonaccialmostconvergentsequencespaceandFibonaccicore.Kyungpook Math. J. 55, 355-372 (2015). ̇ [10] Demiriz, S., Ilkhan, M., Kara E.E.: Almost convergence and Euler totient matrix. Ann Funct Anal. 2020 1–13. ̇ [11] Ilkhan, M.: Certain geometric properties and matrix transformations on a newly introduced Banach space. Fundam. J. Math. Appl. 3(1), 45-51 (2020). ̇ ̇ [13] Ilkhan Kara, M., Bayrakdar, M.A.: A study on matrix domain of Riesz-Euler totient matrix in the space of p-absolutely summable sequences. Commun. Adv. Math. Sci. 4(1), 14-25 (2021). ̇
  • [15] Polat, H.: Some new Pascal sequence spaces. Fundam. J. Math. Appl., 1(1), 61-68 (2018).
  • [16] Aydın,S., Polat, H.: Difference sequence spaces derived by using Pascal transform. Fundam. J. Math. Appl., 2(1), 56-62 (2019).
  • [17] Erdem, S., Demiriz, S.: A study on strongly almost convergent and strongly almost null binomial double sequence spaces. Fundam. J. Math. Appl., 4(4), 271-279 (2021).
  • [18] Candan,M.:AnewaspectforsomesequencespacesderivedusingthedomainofthematrixB.Fundam.J.Math.Appl., 5(1), 51-62 (2022).
  • [19] Khan,V.A.,Abdullah,S.A.,Alshlool,K.M.:ParanormidealconvergentFibonaccidifferencesequencespaces.Commun. Adv. Math. Sci., 2(4), 293-302 (2019).
  • [20]Ellidokuzog ̆lu,H.B.,Demiriz,S.,Köseog ̆lu,A.:Ontheparanormedbinomialsequencespaces.Univers.J.Math. Appl., 1(3), 137-147 (2018).
  • [21] Polat, H.: Some new Cauchy sequence spaces. Univers. J. Math. Appl., 1(4), 267-272 (2018).
  • [22] Roopaei, H., Yaying, T.: Quasi-Cesaro matrix and associated sequence spaces. Turkish J. Math., 45(1), 153-166 (2021).
  • [23] Yaying, T., Hazarika, B.: On sequence spaces defined by the domain of a regular Tribonacci matrix. Math. Slovaca, 70(3), 697-706 (2020).
  • [24] Mursaleen, M., Roopaei, H.: Sequence spaces associated with fractional Copson matrix and compact operators. Results in Math., 76, 1-20 (2021).
  • [25] Roopaei, H., Bas ̧ar, F.: On the spaces of Cesaro absolutely p-summable, null, and convergent sequences. Math. Meth. Appl. Sci., 44(5), 3670-3685 (2021).
  • [26] Cooke,R.G.: InfiniteMatricesandSequenceSpaces,Mcmillan,NewYork(1950).
  • [27] Shcherbakov, A. A.: Kernels of sequences of complex numbers and their regular transformations. Math. Notes. 22, 948-953 (1977).
  • [28] Steinhaus, H.: Quality control by sampling. Collog. Math. 2, 98-108 (1951).
  • [29] Fridy, J.A., Orhan, C.: Statistical core theorems. J. Math. Anal. Appl. 208, 520-527 (1997).
  • [30] Simons, S.: Banach limits, infinite matrices and sublinear functionals. J. Math. Anal. Appl. 26, 640-655 (1969).
  • [31] Connor, J., Fridy, J. A., Orhan, C.: Core equality results for sequences. J. Math. Anal. Appl. 321, 515-523 (2006).
  • [32] Demiriz, S., Çakan, C.: On some new paranormed Euler sequence spaces and Euler core. Acta Math. Sin. (Engl. Ser.). 26, 1207–1222 (2010).
  • [33] Demiriz, S. Çakan, C.: Some new paranormed difference sequence spaces and weighted core. Comput. Math. Appl. 64, 1726-1739 (2012).
  • [34] Demiriz, S., Çakan, C.: Some new paranormed sequence spaces and α-core of a sequence. Pure Appl. Math. Letters. 2016, 32-45 (2016). ̇ [35] Ilkhan, M., Simsek, N., Kara, E.E.: A new regular infinite matrix defined by Jordan totient function and its matrix domain in lp. Math. Methods Appl. Sci. 44(9), 7622-7633 (2021).
  • [36] Sıddıqi,J.A.Infinitematricessummingeveryalmostperiodicsequences.Pacific.J.Math.39(1),235-251(1971). ̇ [37] Kara, E.E., Ilkhan, M., Simsek, N.: A study on certain sequence spaces using Jordan totient function, 8th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2019), August 27-30, 2019, Baku, Azerbaijan.
  • [38] Demirci, K.: A-statistical core of a sequence. Demonstratio Math. 33, 43-51 (200

Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences

Year 2022, , 199 - 207, 22.12.2022
https://doi.org/10.36753/mathenot.1022886

Abstract

In this paper, the notion of almost convergence is used to obtain a space as the domain of a regular matrix. After defining a new type of core for
complex-valued sequences, certain inclusion theorems are proved.

References

  • [1] Lorentz, G.G.: A contribution to the theory of divergent sequences. Acta Math. 80, 167-190 (1948).
  • [2] Bas ̧ar,F.,Kiris ̧çi,M.:Almostconvergenceandgeneralizeddifferencematrix.Comput.Math.Appl.61,602-611(2011).
  • [3] Kiris ̧çi, M.: Almost convergence and generalized weighted mean II. J. Inequal. Appl. 2014 93, (2014).
  • [4] Kiris ̧çi, M.: The spaces of Euler almost null and Euler almost convergent sequences. Commun. Fac. Sci. Univ. Ank. Series A1. 62(2), 85-100 (2013).
  • [5] Mursaleen, M.: Invariant means and some matrix transformations. Indian J. Pure Appl. Math. 25(3), 353-359 (1994).
  • [6] Bas ̧ar, F., Çolak, R.: Almost-conservative matrix transformations. Turkish J. Math. 13(3), 91-100 (1989).
  • [7] Bas ̧ar, F.: f−conservative matrix sequences. Tamkang J. Math. 22(2), 205-212 (1991).
  • [8] Qamaruddin, Q., Mohuiddine, S.A.: Almost convergence and some matrix transformations. Filomat. 21(2), 261-266 (2007).
  • [9] Demiriz,S.,Kara,E.E.,Bas ̧arir,M.:OntheFibonaccialmostconvergentsequencespaceandFibonaccicore.Kyungpook Math. J. 55, 355-372 (2015). ̇ [10] Demiriz, S., Ilkhan, M., Kara E.E.: Almost convergence and Euler totient matrix. Ann Funct Anal. 2020 1–13. ̇ [11] Ilkhan, M.: Certain geometric properties and matrix transformations on a newly introduced Banach space. Fundam. J. Math. Appl. 3(1), 45-51 (2020). ̇ ̇ [13] Ilkhan Kara, M., Bayrakdar, M.A.: A study on matrix domain of Riesz-Euler totient matrix in the space of p-absolutely summable sequences. Commun. Adv. Math. Sci. 4(1), 14-25 (2021). ̇
  • [15] Polat, H.: Some new Pascal sequence spaces. Fundam. J. Math. Appl., 1(1), 61-68 (2018).
  • [16] Aydın,S., Polat, H.: Difference sequence spaces derived by using Pascal transform. Fundam. J. Math. Appl., 2(1), 56-62 (2019).
  • [17] Erdem, S., Demiriz, S.: A study on strongly almost convergent and strongly almost null binomial double sequence spaces. Fundam. J. Math. Appl., 4(4), 271-279 (2021).
  • [18] Candan,M.:AnewaspectforsomesequencespacesderivedusingthedomainofthematrixB.Fundam.J.Math.Appl., 5(1), 51-62 (2022).
  • [19] Khan,V.A.,Abdullah,S.A.,Alshlool,K.M.:ParanormidealconvergentFibonaccidifferencesequencespaces.Commun. Adv. Math. Sci., 2(4), 293-302 (2019).
  • [20]Ellidokuzog ̆lu,H.B.,Demiriz,S.,Köseog ̆lu,A.:Ontheparanormedbinomialsequencespaces.Univers.J.Math. Appl., 1(3), 137-147 (2018).
  • [21] Polat, H.: Some new Cauchy sequence spaces. Univers. J. Math. Appl., 1(4), 267-272 (2018).
  • [22] Roopaei, H., Yaying, T.: Quasi-Cesaro matrix and associated sequence spaces. Turkish J. Math., 45(1), 153-166 (2021).
  • [23] Yaying, T., Hazarika, B.: On sequence spaces defined by the domain of a regular Tribonacci matrix. Math. Slovaca, 70(3), 697-706 (2020).
  • [24] Mursaleen, M., Roopaei, H.: Sequence spaces associated with fractional Copson matrix and compact operators. Results in Math., 76, 1-20 (2021).
  • [25] Roopaei, H., Bas ̧ar, F.: On the spaces of Cesaro absolutely p-summable, null, and convergent sequences. Math. Meth. Appl. Sci., 44(5), 3670-3685 (2021).
  • [26] Cooke,R.G.: InfiniteMatricesandSequenceSpaces,Mcmillan,NewYork(1950).
  • [27] Shcherbakov, A. A.: Kernels of sequences of complex numbers and their regular transformations. Math. Notes. 22, 948-953 (1977).
  • [28] Steinhaus, H.: Quality control by sampling. Collog. Math. 2, 98-108 (1951).
  • [29] Fridy, J.A., Orhan, C.: Statistical core theorems. J. Math. Anal. Appl. 208, 520-527 (1997).
  • [30] Simons, S.: Banach limits, infinite matrices and sublinear functionals. J. Math. Anal. Appl. 26, 640-655 (1969).
  • [31] Connor, J., Fridy, J. A., Orhan, C.: Core equality results for sequences. J. Math. Anal. Appl. 321, 515-523 (2006).
  • [32] Demiriz, S., Çakan, C.: On some new paranormed Euler sequence spaces and Euler core. Acta Math. Sin. (Engl. Ser.). 26, 1207–1222 (2010).
  • [33] Demiriz, S. Çakan, C.: Some new paranormed difference sequence spaces and weighted core. Comput. Math. Appl. 64, 1726-1739 (2012).
  • [34] Demiriz, S., Çakan, C.: Some new paranormed sequence spaces and α-core of a sequence. Pure Appl. Math. Letters. 2016, 32-45 (2016). ̇ [35] Ilkhan, M., Simsek, N., Kara, E.E.: A new regular infinite matrix defined by Jordan totient function and its matrix domain in lp. Math. Methods Appl. Sci. 44(9), 7622-7633 (2021).
  • [36] Sıddıqi,J.A.Infinitematricessummingeveryalmostperiodicsequences.Pacific.J.Math.39(1),235-251(1971). ̇ [37] Kara, E.E., Ilkhan, M., Simsek, N.: A study on certain sequence spaces using Jordan totient function, 8th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2019), August 27-30, 2019, Baku, Azerbaijan.
  • [38] Demirci, K.: A-statistical core of a sequence. Demonstratio Math. 33, 43-51 (200
There are 31 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Merve İlkhan Kara 0000-0002-0831-1474

Gizemnur Örnek 0000-0001-7339-7502

Publication Date December 22, 2022
Submission Date December 1, 2021
Acceptance Date November 4, 2022
Published in Issue Year 2022

Cite

APA İlkhan Kara, M., & Örnek, G. (2022). Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences. Mathematical Sciences and Applications E-Notes, 10(4), 199-207. https://doi.org/10.36753/mathenot.1022886
AMA İlkhan Kara M, Örnek G. Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences. Math. Sci. Appl. E-Notes. December 2022;10(4):199-207. doi:10.36753/mathenot.1022886
Chicago İlkhan Kara, Merve, and Gizemnur Örnek. “Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences”. Mathematical Sciences and Applications E-Notes 10, no. 4 (December 2022): 199-207. https://doi.org/10.36753/mathenot.1022886.
EndNote İlkhan Kara M, Örnek G (December 1, 2022) Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences. Mathematical Sciences and Applications E-Notes 10 4 199–207.
IEEE M. İlkhan Kara and G. Örnek, “Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences”, Math. Sci. Appl. E-Notes, vol. 10, no. 4, pp. 199–207, 2022, doi: 10.36753/mathenot.1022886.
ISNAD İlkhan Kara, Merve - Örnek, Gizemnur. “Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences”. Mathematical Sciences and Applications E-Notes 10/4 (December 2022), 199-207. https://doi.org/10.36753/mathenot.1022886.
JAMA İlkhan Kara M, Örnek G. Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences. Math. Sci. Appl. E-Notes. 2022;10:199–207.
MLA İlkhan Kara, Merve and Gizemnur Örnek. “Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences”. Mathematical Sciences and Applications E-Notes, vol. 10, no. 4, 2022, pp. 199-07, doi:10.36753/mathenot.1022886.
Vancouver İlkhan Kara M, Örnek G. Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences. Math. Sci. Appl. E-Notes. 2022;10(4):199-207.

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